1. Technical Field of the Invention
This invention relates generally to the field of signal analysis and synthesis whereby electronic signals are decomposed into independent frequency components, processed, and reconstituted. The invention relates more specifically to signal analysis methods and means which minimize the undesired products or “artifacts” of aforesaid signal analysis and synthesis.
The acquisition of an analog signal often results in a digital sequence, x(n), that contains not only the signal of interest, but also other signals of interest, and/or additive distortion. In the case that the lower band of frequencies are retained, the sequence can be low-pass filtered by a filter h(n) asyl(n)=x(n)*h(n),  (1)where the * symbol represents convolution. Subsequently the result is decimated by M to formyld(n)≡yl(m),m=no+nM  (2)with n, and M integers. The offset, no, is an arbitrary integer value between 0 and M−1 inclusive. It is assumed that M>1 is chosen together with the low-pass cut-off frequency, to achieve an acceptable maximum level of aliasing distortion, while simultaneously minimizing the output sample rate.
The offset, no, is not normally an accessible parameter. Thus the notion of multiple phases associated with the resulting output sampling; i.e, the set of possible outputs represents a poly-phase system. In this example there exist M possible outcomes of the low-pass filter and decimation system. When one additionally considers the use of finite-impulse-response (FIR) filters, it can be easily shown that alternatively, the decimation can occur before the filtering to achieve the same result. Computationally this is very important, especially when only 1 of the M output channels of a particular sample phase, is needed. This concept is extended by the poly-phase filter bank, to allow for computationally efficient frequency channelization. Such poly-phase architectures inherently translate the frequency response of the low-pass filter prototype, h(n). This results in the desired M-channel filter bank.
2. Prior Art
A Discrete Fourier Transform poly-phase filter architecture is presented in FIG. 1. This particular architecture is referred to as the Modified DFT (MDFT) filter bank [1] and is representative of the prior state-of-the-art. The MDFT filter bank combines the key characteristics of DFT filter banks of linear phase analysis and synthesis filters, efficient realization and inherent alias cancellation for near perfect reconstruction. A particular disadvantage of this and related prior art techniques, however, is the need to maintain signal fidelity between the IDFT and DFT operations, shown as dashed lines in the figure. Fidelity is required to maintain alias cancellation. This precludes the use of such prior art MDFT filter banks in certain equalization and data compression applications. Another disadvantage of the prior art is the additional computational complexity shown between the IDFT and DFT operations, which include multiplications and selection of real (Re) and imaginary (Im) signal components.